It isn't clear to me what's the cause of the exhaust gas oxygen sensors (zirconia-based) continually switching high and low. Is this a result of fuel manipulations by the control system, or would the output swing this way even if fuel input were held rock steady? Can the output be used to diagnose engine driveability problems? Maybe one would have to shut off the fuel cycling system if that's what's causing the cycle in order to use the output diagnostically?

The switching style Zirconia sensor design causes it to switch at stoic. It's the fuel control system that is manipulating the mixture that makes it switch back and forth. This is closed loop fuel control. The control system takes away fuel when O2 signal is rich and adds when it's lean. If the O2 signal is steady high or low, you have no idea how rich or lean it is. The signal is only useful when it switches.

Of course the output can be used for you do diagnose fuel issues. Combined with the scan data PCM fuel trim numbers you can determine if, for example, a lean condition is due to a PCM control issue or a fuel delivery issue. If a good O2 is signaling lean and the PCM says it's adding fuel, then you have a supply problem. If the PCM says it's taking fuel away, then you have a control/inputs issue.

The GM Tech 1 scan tool is the designated device to read fuel trim values for my vehicle. Can these numbers be accessed any other way, for instance with a Picoscope device? I haven't bought any kind of code reader either since the car will blink out the codes on the check engine light.

You need a scan tool to access PCM data stream. You can look at the raw serial data with PicoScope, but it would be like listening to a PC modem hooking up. You know its talking, but you have no idea what it's saying. You'll see the data pulses. That can be useful if your scan tool will not communicate. You'll know the vehicle is sending data, but that's all.

There are many options for scan tools. Some are PC based. These options and functionality will be different depending on your world region.